where \(\nu \)  and \(Q\)  are parameters of the reduction.
\(\nu \)  is called the equivariant parameter.
In the non-equivariant limit as \(\nu \rightarrow 0\) ,
the reduced system turns into the bigraded Toda hierarchy
of type \((a,b)\)  [1]}.
\(Q\)  is related to the particular solution
that we shall consider later on.
